Higgs Branch and VOA of 4d $\mathcal{N}=2$ SCFTs from IIB

TL;DR

This paper explores the Higgs branch and vertex operator algebras of 4d $ =2$ SCFTs via IIB string theory on singularities, proposing new examples and computational methods for their structures.

Contribution

It introduces novel methods to derive Higgs branches from singularities, proposes new SCFT examples with E-type Higgs branches, and predicts associated VOAs and BPS quivers.

Findings

Derived Higgs branches from small resolutions of singularities.

Proposed affine E-type W-algebras as VOAs for new SCFTs.

Predicted BPS quivers for specific singularities.

Abstract

We study the Higgs branch and associated vertex operator algebra (VOA) of 4d $\mathcal{N}=2$ superconformal field theories (SCFTs) from the geometric engineering of IIB superstring on canonical threefold singularities. For terminal singularities, we explain how to derive the 4d Higgs branch from their small resolution. We also investigate singularities with compact 4-cycles in their crepant resolution, and discuss different ways to compute their Higgs branch. Using a symplectic duality argument, we propose the first examples of 4d $\mathcal{N}=2$ SCFTs with the E-type Kleinian singularities as their Higgs branches, and conjecture their associated VOA to be affine E-type W-algebra. Many new VOAs with no known W-algebra descriptions are found, with conjectured associated varieties. We investigate the singularities associated with lisse VOAs and propose predictions for the BPS quivers of $D_N^N[k]$ and $E_7^{14}[k]$ from the perspective of deformed singularities. We further analyze the structure of the Schur index using the Coulomb branch IR formula, derive the expressions for the Schur index corresponding to these two classes of singularities, and illustrate, in a general setting, how the Schur index is determined by the BPS quiver.